A weight is suspended on a system of springs and ascillates up and down according to

P=1/10[sin (2t) + sin t]

where P is the position in meters above or below the point of equilibrium (P=0) and t is time is seconds. Find the time when the weight is at equilibrium. Find the exact values (w/out a calc!). (There are 4 solutions). Hint: Set each factor equal to 0.

*** DOn't even know where to start!! UUuugghhh!

No? OK... this is not looking good for me!

Set the equation equal to 0 and find t.

\frac{1}{10}\left(sin(2t)+sin(t)\right)=0

Multiply through by 10:

sin(2t)+sin(t)=0

Now, do you know Newton's method? That would be handy about now. If not, let me know.

Also, if we assume sin(t)\neq 0, we could write:

2sin(t)cos(t)=-sin(t) by using the identity sin(2t)=2sin(t)cos(t)

Now, all one needs to do is divide by sin(t) and finish up.

I do not know newton's method, nor do I need to I don't think. Even if it is handy to know, if I use it, it will not help me with any other problems... I am still kind of lost though, even after your explanation... sorry/thanks

after trying it again, I came up with cos(t)=-1/2. supposedly there are 4 answers? Are they (-pi/3), (2pi/3), (4pi/3), and (-5pi/3)??

Does cos(\frac{-\pi}{3})=\frac{-1}{2}?

Does cos(\frac{2\pi}{3})=\frac{-1}{2}?

Check them and see.

No, they don't even register on my calc. thanks. How would I go about finding the other two??

Galactus, can you look over the wording of this question again and try to help me make sense of what my professor might mean by "there are four possible solutions"?? That would really help, thanks!

The 4 solutions of \frac{1}{10}(sin(2t)+sin(t))=0 over the interval

0\leq x\leq2{\pi}, are:

0, \;\ \frac{4{\pi}}{3}, \;\ \frac{2{\pi}}{3}, \;\ 2{\pi}

Not to complicate things, but what exactly does your professor mean by "Find the time when the weight is at equilibrium?" I'm not sure that this means you should solve for P=0, because to me "in equilibrium" means that the net forces acting on the weight = 0. Which means the acceleration of P is 0, so you want to solve for P''(t) = 0 ; that is, the second derivate of P(t) = 0. This leads to:

4 sin(2t) + sin(t) = 0.

The 4 solutions for this are 0, pi, and the two solutions for cos(t) = -1/8.

Ha! I guess I will find out what she means tomorrow. Thank you though guys!